% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Fundamental_Theorem_Algebra/prob_1096__5378274_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:51.151

% Could-be-implicit typings (1)
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (10)
thf(sy_c_Groups_Ominus__class_Ominus_001tf__a, type,
    minus_minus_a : a > a > a).
thf(sy_c_Groups_Oone__class_Oone_001tf__a, type,
    one_one_a : a).
thf(sy_c_Groups_Oplus__class_Oplus_001tf__a, type,
    plus_plus_a : a > a > a).
thf(sy_c_Groups_Otimes__class_Otimes_001tf__a, type,
    times_times_a : a > a > a).
thf(sy_c_Groups_Ouminus__class_Ouminus_001tf__a, type,
    uminus_uminus_a : a > a).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
thf(sy_v_a, type,
    a2 : a).
thf(sy_v_b, type,
    b : a).
thf(sy_v_x, type,
    x : a).
thf(sy_v_y, type,
    y : a).

% Relevant facts (65)
thf(fact_0_diff__self, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % diff_self
thf(fact_1_diff__0__right, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_0_right
thf(fact_2_diff__zero, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_zero
thf(fact_3_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_4_mult__zero__left, axiom,
    ((![A : a]: ((times_times_a @ zero_zero_a @ A) = zero_zero_a)))). % mult_zero_left
thf(fact_5_mult__zero__right, axiom,
    ((![A : a]: ((times_times_a @ A @ zero_zero_a) = zero_zero_a)))). % mult_zero_right
thf(fact_6_mult__eq__0__iff, axiom,
    ((![A : a, B : a]: (((times_times_a @ A @ B) = zero_zero_a) = (((A = zero_zero_a)) | ((B = zero_zero_a))))))). % mult_eq_0_iff
thf(fact_7_mult__cancel__left, axiom,
    ((![C : a, A : a, B : a]: (((times_times_a @ C @ A) = (times_times_a @ C @ B)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_left
thf(fact_8_mult__cancel__right, axiom,
    ((![A : a, C : a, B : a]: (((times_times_a @ A @ C) = (times_times_a @ B @ C)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_right
thf(fact_9_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_10_mult_Oleft__commute, axiom,
    ((![B : a, A : a, C : a]: ((times_times_a @ B @ (times_times_a @ A @ C)) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % mult.left_commute
thf(fact_11_mult_Ocommute, axiom,
    ((times_times_a = (^[A2 : a]: (^[B2 : a]: (times_times_a @ B2 @ A2)))))). % mult.commute
thf(fact_12_mult_Oassoc, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % mult.assoc
thf(fact_13_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_14_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : a, C : a, B : a]: ((minus_minus_a @ (minus_minus_a @ A @ C) @ B) = (minus_minus_a @ (minus_minus_a @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_15_diff__eq__diff__eq, axiom,
    ((![A : a, B : a, C : a, D : a]: (((minus_minus_a @ A @ B) = (minus_minus_a @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_16_mult__right__cancel, axiom,
    ((![C : a, A : a, B : a]: ((~ ((C = zero_zero_a))) => (((times_times_a @ A @ C) = (times_times_a @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_17_mult__left__cancel, axiom,
    ((![C : a, A : a, B : a]: ((~ ((C = zero_zero_a))) => (((times_times_a @ C @ A) = (times_times_a @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_18_no__zero__divisors, axiom,
    ((![A : a, B : a]: ((~ ((A = zero_zero_a))) => ((~ ((B = zero_zero_a))) => (~ (((times_times_a @ A @ B) = zero_zero_a)))))))). % no_zero_divisors
thf(fact_19_divisors__zero, axiom,
    ((![A : a, B : a]: (((times_times_a @ A @ B) = zero_zero_a) => ((A = zero_zero_a) | (B = zero_zero_a)))))). % divisors_zero
thf(fact_20_mult__not__zero, axiom,
    ((![A : a, B : a]: ((~ (((times_times_a @ A @ B) = zero_zero_a))) => ((~ ((A = zero_zero_a))) & (~ ((B = zero_zero_a)))))))). % mult_not_zero
thf(fact_21_eq__iff__diff__eq__0, axiom,
    (((^[Y : a]: (^[Z : a]: (Y = Z))) = (^[A2 : a]: (^[B2 : a]: ((minus_minus_a @ A2 @ B2) = zero_zero_a)))))). % eq_iff_diff_eq_0
thf(fact_22_right__diff__distrib_H, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ A @ (minus_minus_a @ B @ C)) = (minus_minus_a @ (times_times_a @ A @ B) @ (times_times_a @ A @ C)))))). % right_diff_distrib'
thf(fact_23_left__diff__distrib_H, axiom,
    ((![B : a, C : a, A : a]: ((times_times_a @ (minus_minus_a @ B @ C) @ A) = (minus_minus_a @ (times_times_a @ B @ A) @ (times_times_a @ C @ A)))))). % left_diff_distrib'
thf(fact_24_right__diff__distrib, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ A @ (minus_minus_a @ B @ C)) = (minus_minus_a @ (times_times_a @ A @ B) @ (times_times_a @ A @ C)))))). % right_diff_distrib
thf(fact_25_left__diff__distrib, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ (minus_minus_a @ A @ B) @ C) = (minus_minus_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ C)))))). % left_diff_distrib
thf(fact_26_inf__period_I1_J, axiom,
    ((![P : a > $o, D2 : a, Q : a > $o]: ((![X2 : a, K : a]: ((P @ X2) = (P @ (minus_minus_a @ X2 @ (times_times_a @ K @ D2))))) => ((![X2 : a, K : a]: ((Q @ X2) = (Q @ (minus_minus_a @ X2 @ (times_times_a @ K @ D2))))) => (![X3 : a, K2 : a]: ((((P @ X3)) & ((Q @ X3))) = (((P @ (minus_minus_a @ X3 @ (times_times_a @ K2 @ D2)))) & ((Q @ (minus_minus_a @ X3 @ (times_times_a @ K2 @ D2)))))))))))). % inf_period(1)
thf(fact_27_inf__period_I2_J, axiom,
    ((![P : a > $o, D2 : a, Q : a > $o]: ((![X2 : a, K : a]: ((P @ X2) = (P @ (minus_minus_a @ X2 @ (times_times_a @ K @ D2))))) => ((![X2 : a, K : a]: ((Q @ X2) = (Q @ (minus_minus_a @ X2 @ (times_times_a @ K @ D2))))) => (![X3 : a, K2 : a]: ((((P @ X3)) | ((Q @ X3))) = (((P @ (minus_minus_a @ X3 @ (times_times_a @ K2 @ D2)))) | ((Q @ (minus_minus_a @ X3 @ (times_times_a @ K2 @ D2)))))))))))). % inf_period(2)
thf(fact_28_mult__cancel__right2, axiom,
    ((![A : a, C : a]: (((times_times_a @ A @ C) = C) = (((C = zero_zero_a)) | ((A = one_one_a))))))). % mult_cancel_right2
thf(fact_29_mult__cancel__right1, axiom,
    ((![C : a, B : a]: ((C = (times_times_a @ B @ C)) = (((C = zero_zero_a)) | ((B = one_one_a))))))). % mult_cancel_right1
thf(fact_30_mult__cancel__left2, axiom,
    ((![C : a, A : a]: (((times_times_a @ C @ A) = C) = (((C = zero_zero_a)) | ((A = one_one_a))))))). % mult_cancel_left2
thf(fact_31_mult__cancel__left1, axiom,
    ((![C : a, B : a]: ((C = (times_times_a @ C @ B)) = (((C = zero_zero_a)) | ((B = one_one_a))))))). % mult_cancel_left1
thf(fact_32_diff__0, axiom,
    ((![A : a]: ((minus_minus_a @ zero_zero_a @ A) = (uminus_uminus_a @ A))))). % diff_0
thf(fact_33_add_Oleft__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % add.left_neutral
thf(fact_34_add_Oright__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.right_neutral
thf(fact_35_add__cancel__left__left, axiom,
    ((![B : a, A : a]: (((plus_plus_a @ B @ A) = A) = (B = zero_zero_a))))). % add_cancel_left_left
thf(fact_36_add__cancel__left__right, axiom,
    ((![A : a, B : a]: (((plus_plus_a @ A @ B) = A) = (B = zero_zero_a))))). % add_cancel_left_right
thf(fact_37_add__cancel__right__left, axiom,
    ((![A : a, B : a]: ((A = (plus_plus_a @ B @ A)) = (B = zero_zero_a))))). % add_cancel_right_left
thf(fact_38_add__cancel__right__right, axiom,
    ((![A : a, B : a]: ((A = (plus_plus_a @ A @ B)) = (B = zero_zero_a))))). % add_cancel_right_right
thf(fact_39_add_Oinverse__neutral, axiom,
    (((uminus_uminus_a @ zero_zero_a) = zero_zero_a))). % add.inverse_neutral
thf(fact_40_neg__0__equal__iff__equal, axiom,
    ((![A : a]: ((zero_zero_a = (uminus_uminus_a @ A)) = (zero_zero_a = A))))). % neg_0_equal_iff_equal
thf(fact_41_neg__equal__0__iff__equal, axiom,
    ((![A : a]: (((uminus_uminus_a @ A) = zero_zero_a) = (A = zero_zero_a))))). % neg_equal_0_iff_equal
thf(fact_42_mult_Oleft__neutral, axiom,
    ((![A : a]: ((times_times_a @ one_one_a @ A) = A)))). % mult.left_neutral
thf(fact_43_mult_Oright__neutral, axiom,
    ((![A : a]: ((times_times_a @ A @ one_one_a) = A)))). % mult.right_neutral
thf(fact_44_add__diff__cancel, axiom,
    ((![A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ B) @ B) = A)))). % add_diff_cancel
thf(fact_45_diff__add__cancel, axiom,
    ((![A : a, B : a]: ((plus_plus_a @ (minus_minus_a @ A @ B) @ B) = A)))). % diff_add_cancel
thf(fact_46_add__diff__cancel__left, axiom,
    ((![C : a, A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ C @ A) @ (plus_plus_a @ C @ B)) = (minus_minus_a @ A @ B))))). % add_diff_cancel_left
thf(fact_47_add__diff__cancel__left_H, axiom,
    ((![A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ B) @ A) = B)))). % add_diff_cancel_left'
thf(fact_48_add__diff__cancel__right, axiom,
    ((![A : a, C : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ C) @ (plus_plus_a @ B @ C)) = (minus_minus_a @ A @ B))))). % add_diff_cancel_right
thf(fact_49_add__diff__cancel__right_H, axiom,
    ((![A : a, B : a]: ((minus_minus_a @ (plus_plus_a @ A @ B) @ B) = A)))). % add_diff_cancel_right'
thf(fact_50_mult__minus__left, axiom,
    ((![A : a, B : a]: ((times_times_a @ (uminus_uminus_a @ A) @ B) = (uminus_uminus_a @ (times_times_a @ A @ B)))))). % mult_minus_left
thf(fact_51_minus__mult__minus, axiom,
    ((![A : a, B : a]: ((times_times_a @ (uminus_uminus_a @ A) @ (uminus_uminus_a @ B)) = (times_times_a @ A @ B))))). % minus_mult_minus
thf(fact_52_mult__minus__right, axiom,
    ((![A : a, B : a]: ((times_times_a @ A @ (uminus_uminus_a @ B)) = (uminus_uminus_a @ (times_times_a @ A @ B)))))). % mult_minus_right
thf(fact_53_minus__diff__eq, axiom,
    ((![A : a, B : a]: ((uminus_uminus_a @ (minus_minus_a @ A @ B)) = (minus_minus_a @ B @ A))))). % minus_diff_eq
thf(fact_54_add_Oright__inverse, axiom,
    ((![A : a]: ((plus_plus_a @ A @ (uminus_uminus_a @ A)) = zero_zero_a)))). % add.right_inverse
thf(fact_55_add_Oleft__inverse, axiom,
    ((![A : a]: ((plus_plus_a @ (uminus_uminus_a @ A) @ A) = zero_zero_a)))). % add.left_inverse
thf(fact_56_uminus__add__conv__diff, axiom,
    ((![A : a, B : a]: ((plus_plus_a @ (uminus_uminus_a @ A) @ B) = (minus_minus_a @ B @ A))))). % uminus_add_conv_diff
thf(fact_57_diff__minus__eq__add, axiom,
    ((![A : a, B : a]: ((minus_minus_a @ A @ (uminus_uminus_a @ B)) = (plus_plus_a @ A @ B))))). % diff_minus_eq_add
thf(fact_58_group__cancel_Osub2, axiom,
    ((![B3 : a, K3 : a, B : a, A : a]: ((B3 = (plus_plus_a @ K3 @ B)) => ((minus_minus_a @ A @ B3) = (plus_plus_a @ (uminus_uminus_a @ K3) @ (minus_minus_a @ A @ B))))))). % group_cancel.sub2
thf(fact_59_add__eq__0__iff, axiom,
    ((![A : a, B : a]: (((plus_plus_a @ A @ B) = zero_zero_a) = (B = (uminus_uminus_a @ A)))))). % add_eq_0_iff
thf(fact_60_ab__group__add__class_Oab__left__minus, axiom,
    ((![A : a]: ((plus_plus_a @ (uminus_uminus_a @ A) @ A) = zero_zero_a)))). % ab_group_add_class.ab_left_minus
thf(fact_61_add_Oinverse__unique, axiom,
    ((![A : a, B : a]: (((plus_plus_a @ A @ B) = zero_zero_a) => ((uminus_uminus_a @ A) = B))))). % add.inverse_unique
thf(fact_62_eq__neg__iff__add__eq__0, axiom,
    ((![A : a, B : a]: ((A = (uminus_uminus_a @ B)) = ((plus_plus_a @ A @ B) = zero_zero_a))))). % eq_neg_iff_add_eq_0
thf(fact_63_neg__eq__iff__add__eq__0, axiom,
    ((![A : a, B : a]: (((uminus_uminus_a @ A) = B) = ((plus_plus_a @ A @ B) = zero_zero_a))))). % neg_eq_iff_add_eq_0
thf(fact_64_diff__conv__add__uminus, axiom,
    ((minus_minus_a = (^[A2 : a]: (^[B2 : a]: (plus_plus_a @ A2 @ (uminus_uminus_a @ B2))))))). % diff_conv_add_uminus

% Conjectures (3)
thf(conj_0, hypothesis,
    ((x = zero_zero_a))).
thf(conj_1, hypothesis,
    ((~ ((a2 = zero_zero_a))))).
thf(conj_2, conjecture,
    (((y = zero_zero_a) = ((minus_minus_a @ (times_times_a @ a2 @ y) @ (times_times_a @ b @ x)) = zero_zero_a)))).
